Question

every sixth visitor to an animal shelter gets a free animal calendar every twentieth visitor gets a free animal toy. Which visitor each day will be the first one to get both the calendar and the animal toy?

Answer 1

Here we have a case of the least common multipl(lcm) of 6 and 20.
Prime numbers 2,3,5,7,11,13,17,19... (natural numbers greater than 1 that has no positive divisors other than 1 and itself) .
lcm(6,20)= 6 20 | 2
                  3 10 | 3
                  1 10 | 2
                       5 | 5
                       1
2*3*2*5=60 The first one to get both calendar and the animal toy will be 60th.
 
Explenation: First we look for the smallest prime number with wich 6 and 20 can be devided by. That is 2. Next is 3. Since 10 is not divisible by 3, we only copy it. Under the 6 we got 1, wich is our goal. Now we continue to devide 10 by prime numbers till we also get 1. We now multiple all divisors and we get the least common multiple.